1. Qiang Zhao Theory Division Institute of High Energy Physics, CAS Email: zhaoq@ihep.ac.cn Topics on charmonium hadronic decays Topics on charmonium hadronic decays Univ. of Science and Technology of China June 22, 2007

2. Outline Charm quark and charmonium spectrum “  puzzle” and “12% rule” in J/ ,  ’  V P ( V= , , , K*; P = , , , K) Isospin violations in V  V P, e.g. , J/     0 Scalar glueball search in charmonium hadronic decays Summary

3. Convention (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3; 2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge. Quarks as building blocks of hadrons: meson (qq), baryon (qqq) Quarks are not free due to QCD colour force (colour confinement). Chiral symmetry spontaneous breaking gives masses to quarks. Hadrons, with rich internal structures, are the smallest objects in Nature that cannot be separated to be further finer free particles. Quarks are not free due to QCD colour force (colour confinement). Chiral symmetry spontaneous breaking gives masses to quarks. Hadrons, with rich internal structures, are the smallest objects in Nature that cannot be separated to be further finer free particles.

4. 原子 – 10 –10 m 原子核 – 10 –14 m 核子 ( 质子, 中子 ) – 10 –15 m 核子内部 ( 夸克 - 胶子 ) 自由 度 (0.1~0.5)×10 –15 m 产生新强子 ( , , K…) 电磁探针 光子 E  = 2  ×197.3 MeV·fm/  强子 ( 重子 + 介子 ) 是目前能从物质中分离 出来、具有内部结构的 最小单元。 强子物理 探索物质的微观结构

5. Charm quark and charmonium state c L S=0 cc c L S=1 cc Parity: P=(  1) L+1 Charge conjugate: C=(  1) L+S ………. J/  

6. n=0  c (2980) J/  (3096)  '(3686) 0  (L=0,S=0)1  (L=0,S=1)0  (L=1,S=1) Mass (MeV)  c0 (3414) n=1 Charm quark and charmonium states 1976 Nobel Prize: B. Richter and S. C.-C. Ting "for their pioneering work in the discovery of a heavy elementary particle of a new kind"

7. J/  ** e+ e- Beijing Electron-Positron Collider Vector meson production in electron-positron collision

8.  c (2980) J/  (3096) 0  (L=0,S=0)1  (L=0,S=1) Mass (MeV) D  D threshold  c (2980)  Light mesons , , K*K, … J/  hadronic decay

9. glue c cc Meson J/  Glue rich intermediate states f0 Lattice QCD prediction Lattice QCD 0 ++ :1.5 ~ 1.7 GeV Exp. Scalars:f0(1370) f0(1500) f0(1710) f0(1790) (?) f0(1810) (?) Meson q qq qq q A probe of strong QCD dynamics Close & Zhao, PRD71, 094022(2005); Zhao, PRD72, 074001 (2005) Why study charmonium hadronic decays?

10. J/  c c uu  dd (I=0) J/  c c  (I=0) ss(I=0)  = (uu+dd)/  2  = ss A flavour filter for Okubo-Zweig-Iizuka (OZI) disconnected transitions V= Structure of the light hadrons: q  q, glueball, multiquark, hybrid … OZI rule violations Isospin violations  (I=0) q  q (I=1)

11. Exclusive decays of J/ ,  '  Vector + Pseudoscalar OZI singly or doubly disconnected process “12% rule” for J/  and  ‘ and “  puzzle” Isospin violated process: , J/ ,  '   0, and its correlation with the OZI-rule violation OZI doubly disconnected process Separate the EM and strong isospin violating processes Focus

12. “12% rule” and “  ” puzzle pQCD expectation of the ratio between J/  and  ' annihilation: “  puzzle” R(  ) = c J/ ,  ' g c c* ** J/ ,  ' c* Large “12% rule” violation in  ! J PC = 1   0.2 %

13. Theoretical explanations: 1. J/    is enhanced J/  -glueball mixing: Freund and Nambu, Hou and Soni, Brodsky, Lepage and Tuan Final state interaction: Li, Bugg and Zou Intrinsic charmonium component within light vectors: Brodsky and Karliner, Feldman and Kroll 2.  '   is suppressed Karl and Roberts: sequential fragmentation model Pinsky: hindered M1 transition model Chaichian and Tornqvist: exponential form factor model Chen and Braaten: color octet Fock state dominance in J/  Rosner:  ' and  " mixing 3. Others …

14. Isospin violation process and its implication c c* V P J/  g c c* V P J/  ** Comparable !? Particle Data Group

15.  3g “12% rule” will not hold if EM transitions are important. Otherwise, interferences from the EM decays with the strong decays are unavoidable. +/  EM + … ** c c* V P J/  ** V P

16. V ( , ,  …) Vector meson dominance model V  * coupling: EM field in terms of vector meson fields:  ** e+ e- ** e+ e-  =

17. Vector meson dominance model V  P coupling: V  * coupling: Transition amplitude:

18. I. Determine g V  P in V   P V  P

19. II. Determine e/f V in V  e+ e- V ** e+ e-

20. III. Determine g P  in P   All the relevant data are available ! IV. Form factors Corrections to the V  *P vertices:   P

21. Isospin violated process

22. Isospin violated process

23. For the isospin violated decays, the 12% rule has been violated. One cannot expect the 12% rule to hold in exclusive hadronic decays. For those channels exhibiting large deviations from the empirical 12%, their EM contributions to  '  VP are also relatively large.

24. with Evidence for large EM transition interferences in  : Large branching ratio differences exist between the charged and neutral K*K- bar implies significant isospin violations. A Left = Right =

25. B Left = Right = C Left =Right = D Left = Right =

26. Including EM and strong transitions (G. Li, Q. Z. and C.H. Chang, hep-ph/0701020)

27. For the isospin violated decays, the 12% rule has been violated due to the contributions from the form factor corrections. One cannot expect the 12% rule to hold in exclusive hadronic decays. For those channels exhibiting large deviations from the empirical 12%, their EM contributions to  ’  VP are also relatively large. Interferences from the EM transitions are important in the branching ratio fraction between J/psi and psi-prime. This could be one of the sources causing the large deviations from the empirical 12% rule (Zhao, Li and Chang, PLB645, 173 (2007)). One has to combine the strong interaction in the study of “  puzzle”, and this has been done in a QCD factorization scheme (Li, Zhao and Chang, hep-ph/0701020). A brief summary

28. Two sources: I) Isospin violation via electromagnetic decays EM interaction does not conserve isospin II) Isospin violation in strong decays u and d quark have different masses Correlation with the OZI rule violation Isospin violations in V  V P

29. Isospin violation in     0 s ss  (I=0)  0 (I=1)  (I=0) g ** ss s  (I=0)  0 (I=1)

30. I) EM process in VMD: Isospin violation in     0

31. Decompose the EM field in terms of vector mesons in Process-I:

32. II) Isospin violation in strong decays: Physical vacuum is not invariant under chiral symmetries  Chiral symmetry is spontaneously broken: Current quarks are no longer massless  Chiral symmetry is explicitly broken: m u  m d Manifestations:  Light 0  octet mesons (Goldstone bosons), , K,   Strong isospin violation: m(  0 ) m(K  ); m(p) < m(n) …

33. Strong isospin violation via intermediate meson exchanges If m u = m d, (a)+(b) = 0 and (c)+(d) = 0. If m u  m d, (a)+(b)  0 and (c)+(d)  0. Li, Zhao and Zou, arXiv:0706.0384[hep-ph]

34. Three schemes for the intermediate meson exchange loops 1. On-shell approximation 2. Feynman integration with a monopole form factor 3. Feynman integration with a dipole form factor

35. 1. On-shell approximation 0, No form factor n = 1, monopole 2, dipole  (GeV) : to be determined by experimental data.

36. Numerical results : Experimental branching ratio: On-shell approximation underestimates the data. Exclusive KK(K*) loop

37. EM and KK(K*) out of phase EM and KK(K*) in phase  -dependence of the sum of EM and KK(K*) loop Still underesitmate the experimental data.

38. 2. Feynman integration with a monopole form factor  Similarly for the neutral meson loop …

39.  -dependence of the exclusive KK(K*) loop with a monopole form factor

40.  -dependence of the exclusive KK*(K) loop with a monopole form factor

41. 3. Feynman integration with a dipole form factor Exclusive KK(K*) loop contribution to BR

42. Exclusive KK*(K) loop contribution to BR

43. Inclusive contributions from the isospin violating transitions Isospin violation = EM  Strong decay loops Exp. In phase Out of phase V  V P is a P-wave decay, favors a dipole form factor.

44. The correlation between the OZI-rule violation and strong isospin violations makes the intermediate meson exchange process a possible dynamic solution for separating the EM and the strong isospin violation mechanisms. Application to the study of a 0 (980)-f 0 (980) mixing in J/   a 0 (980)   0 (J.J. Wu, Q.Z. and B.S. Zou, Phys. Rev. D in press). Experimental focuses of BES, CLEO-c, KLOE, B- factories… Summary

45. Thanks !

46. Conventional and unconventional meson Scalar mesons between 1~2 GeV Scalar glueball-q  q mixing Scalar meson production in charmonium hadronic decays Scalar meson structures probed in charmonium hadronic decays

47. Convention (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3; 2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge. Meson spectroscopy I) Q  Q mesons Quarks as building blocks of hadrons: meson (q  q), baryon (qqq)

48. Conventional Q  Q mesons: 1.Mesons are bound state of Q  Q with baryon number B=0; 2.The parity is given by P=(  1) L+1 with orbital angular momentum L; 3.The meson spin J is given by |L  S| < J < | L+S|, where S=0, 1 are the total spin of the quarks. 4. Charge conjugate is defined as C=(  1) L+S for mesons made of quark and its own antiquark. For light quarks: u, d, and s, the SU(3) flavor symmetry constrains the number of flavor Q  Q multiplet: 3   3 = 8  1 34 1 1

49. II) Non-Q  Q mesons Type (a): J PC are not allowed by Q  Q configuration +  L S=1 For states in natural spin-parity series P=(  1) L+1 =(  1) J, the state must have S=1 and hence CP=(  1) (L+S)+(L+1) =+1. Therefore, mesons with natural spin-parity but CP=  1 will be forbidden, e.g. 0 + , 1  +, 2 + , 3  +, … Natural: 0 ++, 1 , 2 ++, 3 , … Unnatural: ( 0  ), 1 ++, 2 ,3 ++, … +  L S=0 Unnatural: 0  +, 1 + , 2  +, 3 + , …

50. Exotic type 1: Mesons have the same J PC as a Q  Q, but cannot be accommodated into the SU(3) nonet: 3   3 = 8  1 3 4 1 1 I=0 f0(980)  (958)  (547)  (782)  (1020)  /f0(600) f0(1370) f0(1500) f0(1710) 0  1  0  Jaffe’s Multiquarks? Meson molecule ? Glueball ? Q  Q-glue mixing ? Mass f0(1790) f0(1810)

51. Experimental signals for scalar mesons Crystal Barrel, WA102, MARKIII, DM2 … Beijing Spectrometer (BES) J/   V f0; f0  PP, J/    f0; f0  PP, VV  cj  f0 f0, f0 f2 V= , , K*,  ; PP = , , , K  K,

52. f 0 (1370) clearly seen in J/   , but not seen in J/   . f 0 (1370) NO f 0 (1370) f 0 (1370) at BES S. Jin, Plenary talk at ICHEP04 f0(1370)  is dominant over K K, ,  ;  nonstrange n  n

53. Clear f 0 (1710) peak in J/    KK. No f 0 (1710) observed in J/    ! f 0 (1710) at BES f 0 (1710) NO f 0 (1710) S. Jin, Plenary talk at ICHEP04 f0(1710)  KK^ is dominant.  s  s

54. J/  c c  uu  dd J/  c c  ss  = (uu+dd)/  2  = ss A flavour filter for OZI singly disconnected transitions: V= f0(1370)f0(1710) Could the exp. puzzle imply correlations between the structure of scalars and their prod. mechanism in J/   V f0 ?

55. glue c cc M J/  Glue rich intermediate states f0 Lattice QCD prediction Morningstar and Peardon, PRD60, 034509 (1999) Interest in scalar glueball search: Mesons are made of colored gluons confined by strong interaction Lattice 0 ++ :1.5 ~ 1.7 GeV Exp. Scalars:f0(1370) f0(1500) f0(1710) f0(1790) (?) f0(1810) (?) M q qq qq q

56. Glueball and Q  Q mixing in the scalar mesons In the basis of |G> = gg, |S> = s  s, and |N> = n  n = (u  u + d  d)/  2, the glueball-quarkonia mixing can be expressed as: S N G Amsler & Close, PLB353, 385(1995); PRD53, 295(1996); Close & Kirk, PLB483, 345(2000). where i=1,2,3, and f 1,2,3 = f0(1710), f0(1500) and f0(1370), respectively.

57. Parameterization of f0  PP g0g0 r2  g0r2  g0 r3  g0r3  g0 f0f0 P P   Partial decay widths for f0  PP: Close & Zhao, PRD71, 094022(2005)

58. S N G Lattice QCD: M G ~ 1.5 – 1.7 GeV f0 states 1710 1370 1500 WA102WA102+BES Strong QCD character.

59. Implications of the OZI-rule violation: ii) OZI rule on f0(1370): br(J/  f0(1370)  K  K)<< br(J/  f0(1370)  ) Exp: br(J/  f0(1370)  ) is dominant !  KKKK gg s  s n  n 0.360.930.09  0.84 0.35  0.41 0.40  0.07  0.91 c c  ss f0(1710) i) OZI rule on f0(1710): br(J/  f0(1710)  K  K) > br(J/  f0(1710)  K  K) Exp: br(J/  f0(1710)  K  K) / br(J/  f0(1710)  K  K) ~ 0.3 !

60. Scalar mesons production in J/   V f 0 c c*  (ss*) f 0 (ss*) c c* J/   (ss*) f 0 (nn*) I) Singly disconnected diagram II) Doubly disconnected diagram III) Glue configuration c c* J/   (ss*) f 0 (gg) pQCD Okubo-Zweig-Iizuka (OZI) rule: I) ~III) ~   II)  =g 2 /4  ~ 0.3 However, a glueball component implies significant OZI-rule violations. g g

61. J/  V ( ,  ) f0f0 P P Factorization of J/   V f 0  V P P Transition amplitudes via potential V  III) I) II) Doubly OZI disconnected Project to the final physical states: Gluon-counting rule: I) ~ III)

62. Partial decay width for J/   V f 0  V P P c c* J/   (ss*) G(gg) c c* J/   (nn*) G(gg) Flavor-blindness of quark-gluon interaction:

63. Step 1 : Direct test of the OZI rule a) OZI rule applies:r  0 b) OZI rule violated:r ~ 1 r = 2.2 where PDG estimate: R exp = 0.75 BES Experiment: br(J/  f0(1710)  KK*) = (2.0  0.7)  10  4 br(J/  f0(1710)  KK*) = (13.2  2.6)  10  4

64. Step 2 : Normalize the G production Normalized glueball production b.r. ratios Scalar decay br. ratios

65. Step 3 : Theoretical predictions for J/  V f0  V KK*, V  The “puzzle” can be explained in the glueball-QQ* mixing scheme, which implies large OZI violation effects in the scalar production. Puzzle  Evidence for the presence of scalar glueball ?

66. OZI violation mechanism for J/   V f 0 Large J/  K*K coupling; Large  K*K coupling; Large f 0 (1710)KKbar coupling c c* J/  K* K K Zhao, Zou & Ma, PLB631, 22(2005), hep-ph/0508088.

67. Intermediate K*K rescattering contributions to J/    f0,  f0

68. Factorization for  c0,2  VV, PP, & SS (a)(b) g 0 : basic gqq* coupling r : OZI-rule violation R : SU(3)f breaking t : glueball coupling strength g0g0 r (c) (d) Zhao, PRD72, 074001 (2005)

69. For a typical state: the transition amplitude is factorized to be: A commonly used form factor:

70. i)  c0,2  V V  c0  c2 BES data Predictions The OZI violation need to be constrained by data for  channel.

71. ii)  c0,2  P P Improved data for  channel are required.

72. Exp. Data from BES for  c0  f 0 (1710) f 0 (1370)  KK . (PRD2005, hep-ex/0508050) normalized Branching ratio fractions a) If OZI-rule is respected, i.e. r  0, will be the smallest decay channel. b) If OZI-rule is violated, i.e. r  1, will be the largest decay channel. iii)  c0,2  f 0 f 0

73. Factorization for  c  VV BES Collaboration, PRD72, 072005(2005).

74. OZI violation mechanism for  c   BES estimate:

75. Summary-1 I. Charmonium hadronic decays are useful for providing additional information about the scalar meson structures. II. The glueball contents are essentially important for interpreting the “puzzling” data from BES for the scalar meson production in J/  decays. III. The strong glueball-QQ* mixings within the scalar mesons imply large OZI violations in J/   V f0, and suggest the crucial role played by the doubly disconnected processes. IV. A possible source for the OZI-rule violation is transitions via intermediate meson rescatterings for which a systematic investigation can be pursued.

76. III. A normalization of the glueball production rate is obtained, which possesses predictive power for the study of the glueball mixing effects in the J/  radiative decay channel and  c0  f 0 f 0. Further experimental data will be useful for establishing these f0 states as glueball-QQ* mixing states: BES, CLEO-c, GSI (?)… Glue-X at JLab? Summary-2